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mathmari

Gold Member

MHB

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Hey!

Let $A$ a $n\times n$ matrix with known LU decomposition, let $u\in \mathbb{R}^n, v\in \mathbb{R}^{n+1}$.

Show that the number of multiplications and divisions that are needed to get a LU decomposition of the $(n+1)\times (n+1)$ matrix $$\begin{pmatrix}A & u \\ v^T\end{pmatrix}$$ is at most $O(n^2)$.

To get $U$, we have to eliminate $n$ terms below the main diagonal (which is the elements of $u^T$ except the last element of that row). Each elimination requires computing the row multiplier, which involves division by the pivotal element.

So we have $n$ divisions, or not? :unsure:

Let $A$ a $n\times n$ matrix with known LU decomposition, let $u\in \mathbb{R}^n, v\in \mathbb{R}^{n+1}$.

Show that the number of multiplications and divisions that are needed to get a LU decomposition of the $(n+1)\times (n+1)$ matrix $$\begin{pmatrix}A & u \\ v^T\end{pmatrix}$$ is at most $O(n^2)$.

To get $U$, we have to eliminate $n$ terms below the main diagonal (which is the elements of $u^T$ except the last element of that row). Each elimination requires computing the row multiplier, which involves division by the pivotal element.

So we have $n$ divisions, or not? :unsure:

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